A thin fixed ring of radius \(a\) has a positive charge \(q\) uniformly distributed over it. A particle of mass \(m\) having a negative charge \(Q\), is placed on the axis at a distance of \(x\) (\(x<<a\)) from the center of the ring. Find the time period of oscillation of the negatively charged particle.

If the answer is of the form \(\huge \delta \pi \sqrt { \frac { \Delta \pi { \varepsilon }_{ o }m{ a }^{ \alpha } }{ qQ } }\), find \( \delta +\Delta +\alpha \).

**Hint**: The motion is *simple harmonic* by nature.

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